Subgroups — #13070898

Order 1408.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622295	C₂	1	2	yes	maximal
2	C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#10622143	C₂	1	4	yes	maximal
4	#66922	—	2	2	no	—
5	C₂×C₁₁×C₁₆	C₂²	1	2	yes	—
6	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	#66882	—	2	2	no	—
8	#66882	C₂²	1	4	yes	—
9	C₂×Dic₂₂	—	4	2	no	—
10	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
11	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
12	C₄²×C₁₁	D₄	1	1	yes	characteristic
13	C₄⋊Dic₁₁	—	2	4	no	—
14	C₄⋊Dic₁₁	—	4	2	no	—
15	C₁₁×C₁₆	Q₈	1	4	yes	complemented
16	#2254	—	11	1	no	maximal, Sylow
17	C₂×C₄×C₁₁	D₈	1	2	yes	—
18	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₁₁	—	4	4	no	—
20	Dic₂₂	—	8	4	no	—
21	C₈×C₁₁	Q₁₆	1	2	yes	—
22	C₈×C₁₁	C₂×Q₈	1	2	yes	—
23	#500	—	11	2	no	—
24	#367	—	11	4	no	—
25	C₄×C₁₆	D₁₁	1	1	yes	characteristic
26	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
27	C₄×C₁₁	SD₃₂	1	4	yes	—
28	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
29	C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
30	Dic₁₁	—	8	4	no	—
31	C₄⋊Q₈	—	22	2	no	—
32	C₂×C₁₆	C₂×D₁₁	1	2	yes	—
33	#107	—	11	4	no	—
34	#107	—	22	2	no	—
35	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
36	C₂×C₁₁	#500	1	1	yes	characteristic
37	C₂×C₁₁	C₂×SD₃₂	1	2	yes	—
38	C₂×Q₈	—	44	2	no	—
39	C₂×C₈	D₄₄	1	1	yes	characteristic
40	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
41	C₄⋊C₄	—	22	4	no	—
42	C₄⋊C₄	—	44	2	no	—
43	C₄²	D₄₄	1	1	yes	characteristic
44	C₁₆	Dic₂₂	1	4	yes	complemented
45	C₁₁	#2254	1	1	yes	characteristic, complemented, Sylow
46	Q₈	—	88	4	no	—
47	C₂×C₄	—	44	4	no	—
48	C₂×C₄	D₈₈	1	2	yes	—
49	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
50	C₈	Dic₄₄	1	2	yes	—
51	C₈	C₂×Dic₂₂	1	2	yes	—
52	C₂²	C₂×D₈₈	1	1	yes	characteristic
53	C₄	—	88	4	no	—
54	C₄	#66864	1	4	yes	—
55	C₄	#66922	1	1	yes	characteristic
56	C₄	C₂×Dic₄₄	1	1	yes	characteristic
57	C₂	#10622295	1	1	yes	characteristic
58	C₂	C₂×#66864	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×C₁₆	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₈
hypercenter	C₄×C₁₆	D₁₁
hypocenter	C₁₁	#2254
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
15. C₁₁×C₁₆	Q₈	semidirect
44. C₁₆	Dic₂₂	semidirect
45. C₁₁	#2254	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10622295	2
C₄×C₁₁×C₁₆	2
#10622143	2
#2254	11